Reduce to lowest terms: $ \dfrac{8}{9} \div \dfrac{2}{3} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{2}{3}$ is $ \dfrac{3}{2}$ Therefore: $ \dfrac{8}{9} \div \dfrac{2}{3} = \dfrac{8}{9} \times \dfrac{3}{2} $ $ \phantom{ \dfrac{8}{9} \times \dfrac{3}{2}} = \dfrac{8 \times 3}{9 \times 2} $ $ \phantom{ \dfrac{8}{9} \times \dfrac{3}{2}} = \dfrac{24}{18} $ The numerator and denominator have a common divisor of $6$, so we can simplify: $ \dfrac{24}{18} = \dfrac{24 \div 6}{18 \div 6} = \dfrac{4}{3} $